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Robust reliable guaranteed cost control of positive interval systems with multiple time delays and actuator failure

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  • Ji-Shi Zhang
  • Yan-Wu Wang
  • Jiang-Wen Xiao
  • Yang Chen

Abstract

This paper addresses the robust reliable guaranteed cost control problem of positive interval systems with multiple time delays and actuator failure for a given quadratic cost function. Through constructing a Lyapunov–Krasovskii functional, a sufficient condition for the existence of robust reliable guaranteed cost controllers is established such that the closed-loop system is positive and asymptotically stable, and the cost function is guaranteed to be no more than a certain upper bound. Based on the linear matrix inequality method, a criterion for the design of robust reliable guaranteed cost controllers is derived which can tolerate all admissible uncertainties as well as actuator failure. Moreover, a convex optimisation problem with linear matrix inequality constraints is formulated to design the optimal robust reliable guaranteed cost controller which minimises the upper bound of the closed-loop system cost. A numerical example is given to show the effectiveness of the proposed methods.

Suggested Citation

  • Ji-Shi Zhang & Yan-Wu Wang & Jiang-Wen Xiao & Yang Chen, 2016. "Robust reliable guaranteed cost control of positive interval systems with multiple time delays and actuator failure," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(4), pages 946-955, March.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:4:p:946-955
    DOI: 10.1080/00207721.2014.911382
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    References listed on IDEAS

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    1. Shen Yin & Steven Ding & Adel Abandan Sari & Haiyang Hao, 2013. "Data-driven monitoring for stochastic systems and its application on batch process," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(7), pages 1366-1376.
    2. Johnson, Charles R., 1974. "Sufficient conditions for D-stability," Journal of Economic Theory, Elsevier, vol. 9(1), pages 53-62, September.
    3. Zhicheng Li & Guanghui Sun & Huijun Gao, 2013. "Guaranteed cost control for discrete-time Markovian jump linear system with time delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(7), pages 1312-1324.
    4. Ali Sghaier Tlili & Sadok Dhbaibi & Naceur Braiek, 2012. "Robust decentralised observer based guaranteed cost control for nonlinear uncertain interconnected systems. Application to multi-machine power systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(9), pages 1713-1727.
    5. Hongyi Li & Yulin Si & Ligang Wu & Xiaoxiang Hu & Huijun Gao, 2011. "Guaranteed cost control with poles assignment for a flexible air-breathing hypersonic vehicle," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(5), pages 863-876.
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    Cited by:

    1. Zhang, Yan & Wang, Fang, 2019. "Adaptive neural control of non-strict feedback system with actuator failures and time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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